Solve 6cos(pi/8)*cos(pi/8)

$$6 \cos ( \frac{ \pi }{ 8 } ) \times \cos ( \frac{ \pi }{ 8 } )$$

Evaluate

$$\frac{3\sqrt{2}}{2}+3\approx 5.121320344$$

Solution Steps

Multiply \cos(\frac{\pi }{8}) and \cos(\frac{\pi }{8}) to get \left(\cos(\frac{\pi }{8})\right)^{2}.

$$6\left(\cos(\frac{\pi }{8})\right)^{2}$$

Get the value of \cos(\frac{\pi }{8}) from trigonometric values table.

$$6\times \left(\frac{\sqrt{\sqrt{2}+2}}{2}\right)^{2}$$

To raise \frac{\sqrt{\sqrt{2}+2}}{2} to a power, raise both numerator and denominator to the power and then divide.

$$6\times \frac{\left(\sqrt{\sqrt{2}+2}\right)^{2}}{2^{2}}$$

Express 6\times \frac{\left(\sqrt{\sqrt{2}+2}\right)^{2}}{2^{2}} as a single fraction.

$$\frac{6\left(\sqrt{\sqrt{2}+2}\right)^{2}}{2^{2}}$$

Calculate \sqrt{\sqrt{2}+2} to the power of 2 and get \sqrt{2}+2.

$$\frac{6\left(\sqrt{2}+2\right)}{2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{6\left(\sqrt{2}+2\right)}{4}$$

Divide 6\left(\sqrt{2}+2\right) by 4 to get \frac{3}{2}\left(\sqrt{2}+2\right).

$$\frac{3}{2}\left(\sqrt{2}+2\right)$$

Use the distributive property to multiply \frac{3}{2} by \sqrt{2}+2.

$$\frac{3}{2}\sqrt{2}+3$$

Factor

$$\frac{3 \sqrt{2} {(\sqrt{2} + 1)}}{2} = 5.121320343559642$$